Yippie!!! I found the problem. Well, someone else tipped me off, THEN I found the problem. I asked around some guys that have the card and have got it working, and was told that (first) the ATI drivers suck, and I should install Lightspeed 2000 drivers. Then, (and I think this was actualy it) I had to remove any old opengl32.dll on the system. I had previously only deleted the one in Windows/system. This must have been it, because now it works (at least in Quake, Quake II and Half-life).
I just wanted to let you guys know that the problem was solved and this thred could be closed.
I appreciate all the info and help. GT, in particular, thanks for the links! That's where I found my fellow saps.(I mean proud ATI Rage Fury owners)

If anyone else was having this problem, and wants any specific help as to what fixed it for me, write Reinheld@mediaone.net since I don't get to check the forums much.
Thanks,
Reinheld
[This message has been edited by Reinheld (edited 08-05-1999).]